Cross correlation using Fast Fourier Transform

[Beliavsky]

To compute the cross correlation at lag p of two 1D arrays of length n you compute sum(x(1+p:n)*y(1:n-p)). If you want the cross correlation at all lags, the Fast Fourier Transform can be used to speed the calculation. Intel describes Implementing the Fourier Correlation Algorithm Using oneAPI. I suggest adding a function ccf(x,y,p) which computes cross correlations from lags 0 to p and uses an FFT when that is the fastest method (which will be for large p).

In general, linear time series analysis and signal processing could be part of stdlib.

[Beliavsky]

A Fortran package that does this is ACFbyFFT, which calls fftw. One could rewrite it to call an FFT that is part of stdlib.